We utilize extreme learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.

翻译：我们利用极限学习机来预测偏微分方程。该方法将状态空间划分为多个窗口，并使用单一模型对每个窗口进行独立预测。尽管仅需少量数据点（在某些情况下，我们的方法可从单个全状态快照中学习），它仍能实现高精度，并在长时间尺度上预测偏微分方程的动态演化。此外，我们展示了如何利用额外对称性来提高样本效率并强制实现等变性。